HASS • HEIL • WEIR
THOMAS’ CALCULUS
FOURTEENTH EDITION
,THOMAS’
CALCULUS FOURTEENTH EDITION
Based on the original work by
GEORGE B. THOMAS, JR.
Massachusetts Institute of Technology
as revised by
JOEL HASS
University of California, Davis
CHRISTOPHER HEIL
Georgia Institute of Technology
MAURICE D. WEIR
Naval Postgraduate School
,Director, Portfolio Management: Deirdre Lynch
Executive Editor: Jeff Weidenaar
Editorial Assistant: Jennifer Snyder
Content Producer: Rachel S. Reeve
Managing Producer: Scott Disanno
Producer: Stephanie Green
TestGen Content Manager: Mary Durnwald
Manager: Content Development, Math: Kristina Evans
Product Marketing Manager: Emily Ockay
Field Marketing Manager: Evan St. Cyr
Marketing Assistants: Jennifer Myers, Erin Rush
Senior Author Support/Technology Specialist: Joe Vetere
Rights and Permissions Project Manager: Gina M. Cheselka
Manufacturing Buyer: Carol Melville, LSC Communications, Inc.
Program Design Lead: Barbara T. Atkinson
Associate Director of Design: Blair Brown
Text and Cover Design, Production Coordination, Composition: Cenveo® Publisher Services
Illustrations: Network Graphics, Cenveo® Publisher Services
Cover Image: Te Rewa Rewa Bridge, Getty Images/Kanwal Sandhu
Copyright © 2018, 2014, 2010 by Pearson Education, Inc. All Rights Reserved. Printed in the United States of
America. This publication is protected by copyright, and permission should be obtained from the publisher prior to
any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms and
the appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit
www.pearsoned.com/permissions/.
Attributions of third party content appear on page C-1, which constitutes an extension of this copyright page.
PEARSON, ALWAYS LEARNING, and MYMATHLAB are exclusive trademarks owned by Pearson Education,
Inc. or its affiliates in the U.S. and/or other countries.
Unless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their
respective owners and any references to third-party trademarks, logos or other trade dress are for demonstrative or
descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement, authorization,
or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and
Pearson Education, Inc. or its affiliates, authors, licensees or distributors.
Library of Congress Cataloging-in-Publication Data
Names: Hass, Joel. | Heil, Christopher, 1960- | Weir, Maurice D.
Title: Thomas’ calculus / based on the original work by George B. Thomas,
Jr., Massachusetts Institute of Technology, as revised by Joel Hass,
University of California, Davis, Christopher Heil,
Georgia Institute of Technology, Maurice D. Weir, Naval Postgraduate
School.
Description: Fourteenth edition. | Boston : Pearson, [2018] | Includes index.
Identifiers: LCCN 2016055262 | ISBN 9780134438986 | ISBN 0134438981
Subjects: LCSH: Calculus--Textbooks. | Geometry, Analytic--Textbooks.
Classification: LCC QA303.2.W45 2018 | DDC 515--dc23 LC record available at https://lccn.loc.gov/2016055262
1 17
Instructor’s Edition
ISBN 13: 978-0-13-443909-9
ISBN 10: 0-13-443909-0
Student Edition
ISBN 13: 978-0-13-443898-6
ISBN 10: 0-13-443898-1
, Contents
Preface ix
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 14
1.3 Trigonometric Functions 21
1.4 Graphing with Software 29
Questions to Guide Your Review 33
Practice Exercises 34
Additional and Advanced Exercises 35
Technology Application Projects 37
2 Limits and Continuity 38
2.1 Rates of Change and Tangent Lines to Curves 38
2.2 Limit of a Function and Limit Laws 45
2.3 The Precise Definition of a Limit 56
2.4 One-Sided Limits 65
2.5 Continuity 72
2.6 Limits Involving Infinity; Asymptotes of Graphs 83
Questions to Guide Your Review 96
Practice Exercises 97
Additional and Advanced Exercises 98
Technology Application Projects 101
3 Derivatives 102
3.1 Tangent Lines and the Derivative at a Point 102
3.2 The Derivative as a Function 106
3.3 Differentiation Rules 115
3.4 The Derivative as a Rate of Change 124
3.5 Derivatives of Trigonometric Functions 134
3.6 The Chain Rule 140
3.7 Implicit Differentiation 148
3.8 Related Rates 153
3.9 Linearization and Differentials 162
Questions to Guide Your Review 174
Practice Exercises 174
Additional and Advanced Exercises 179
Technology Application Projects 182
iii
THOMAS’ CALCULUS
FOURTEENTH EDITION
,THOMAS’
CALCULUS FOURTEENTH EDITION
Based on the original work by
GEORGE B. THOMAS, JR.
Massachusetts Institute of Technology
as revised by
JOEL HASS
University of California, Davis
CHRISTOPHER HEIL
Georgia Institute of Technology
MAURICE D. WEIR
Naval Postgraduate School
,Director, Portfolio Management: Deirdre Lynch
Executive Editor: Jeff Weidenaar
Editorial Assistant: Jennifer Snyder
Content Producer: Rachel S. Reeve
Managing Producer: Scott Disanno
Producer: Stephanie Green
TestGen Content Manager: Mary Durnwald
Manager: Content Development, Math: Kristina Evans
Product Marketing Manager: Emily Ockay
Field Marketing Manager: Evan St. Cyr
Marketing Assistants: Jennifer Myers, Erin Rush
Senior Author Support/Technology Specialist: Joe Vetere
Rights and Permissions Project Manager: Gina M. Cheselka
Manufacturing Buyer: Carol Melville, LSC Communications, Inc.
Program Design Lead: Barbara T. Atkinson
Associate Director of Design: Blair Brown
Text and Cover Design, Production Coordination, Composition: Cenveo® Publisher Services
Illustrations: Network Graphics, Cenveo® Publisher Services
Cover Image: Te Rewa Rewa Bridge, Getty Images/Kanwal Sandhu
Copyright © 2018, 2014, 2010 by Pearson Education, Inc. All Rights Reserved. Printed in the United States of
America. This publication is protected by copyright, and permission should be obtained from the publisher prior to
any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic,
mechanical, photocopying, recording, or otherwise. For information regarding permissions, request forms and
the appropriate contacts within the Pearson Education Global Rights & Permissions department, please visit
www.pearsoned.com/permissions/.
Attributions of third party content appear on page C-1, which constitutes an extension of this copyright page.
PEARSON, ALWAYS LEARNING, and MYMATHLAB are exclusive trademarks owned by Pearson Education,
Inc. or its affiliates in the U.S. and/or other countries.
Unless otherwise indicated herein, any third-party trademarks that may appear in this work are the property of their
respective owners and any references to third-party trademarks, logos or other trade dress are for demonstrative or
descriptive purposes only. Such references are not intended to imply any sponsorship, endorsement, authorization,
or promotion of Pearson’s products by the owners of such marks, or any relationship between the owner and
Pearson Education, Inc. or its affiliates, authors, licensees or distributors.
Library of Congress Cataloging-in-Publication Data
Names: Hass, Joel. | Heil, Christopher, 1960- | Weir, Maurice D.
Title: Thomas’ calculus / based on the original work by George B. Thomas,
Jr., Massachusetts Institute of Technology, as revised by Joel Hass,
University of California, Davis, Christopher Heil,
Georgia Institute of Technology, Maurice D. Weir, Naval Postgraduate
School.
Description: Fourteenth edition. | Boston : Pearson, [2018] | Includes index.
Identifiers: LCCN 2016055262 | ISBN 9780134438986 | ISBN 0134438981
Subjects: LCSH: Calculus--Textbooks. | Geometry, Analytic--Textbooks.
Classification: LCC QA303.2.W45 2018 | DDC 515--dc23 LC record available at https://lccn.loc.gov/2016055262
1 17
Instructor’s Edition
ISBN 13: 978-0-13-443909-9
ISBN 10: 0-13-443909-0
Student Edition
ISBN 13: 978-0-13-443898-6
ISBN 10: 0-13-443898-1
, Contents
Preface ix
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 14
1.3 Trigonometric Functions 21
1.4 Graphing with Software 29
Questions to Guide Your Review 33
Practice Exercises 34
Additional and Advanced Exercises 35
Technology Application Projects 37
2 Limits and Continuity 38
2.1 Rates of Change and Tangent Lines to Curves 38
2.2 Limit of a Function and Limit Laws 45
2.3 The Precise Definition of a Limit 56
2.4 One-Sided Limits 65
2.5 Continuity 72
2.6 Limits Involving Infinity; Asymptotes of Graphs 83
Questions to Guide Your Review 96
Practice Exercises 97
Additional and Advanced Exercises 98
Technology Application Projects 101
3 Derivatives 102
3.1 Tangent Lines and the Derivative at a Point 102
3.2 The Derivative as a Function 106
3.3 Differentiation Rules 115
3.4 The Derivative as a Rate of Change 124
3.5 Derivatives of Trigonometric Functions 134
3.6 The Chain Rule 140
3.7 Implicit Differentiation 148
3.8 Related Rates 153
3.9 Linearization and Differentials 162
Questions to Guide Your Review 174
Practice Exercises 174
Additional and Advanced Exercises 179
Technology Application Projects 182
iii
